Is there a way to add a guest login account on welcome screen of Linux Mint 13 MATE-32bits, similar to the one present in Ubuntu 12.04?
In latest ubuntu which ships lightdm, that supports a guest account,
So install lightdm and replace gdm should work for you, which would do the exactly same thing in Ubuntu 12.04:
apt-get install lightdm
I don't think the simple ability to enable a guest account is natively available in Mint 13. The login manager in 13 uses MDM, which is based on Gnome 2's GDM. In Mint 12, you could just add a couple of lines to a .conf file and you'd be set... but there is a way to do it on Mint 13.
The first step is simple - create a new user (called Guest, if you like).
Next, we need to lock down your home folder so only you can access your files. To do so, open a terminal (while logged in as your main account) and type:
chmod 700 ~
This will change the permissions on your home folder so that only you and root can view it.
You're all done! You now have a second user account that anyone can use, that cannot access your personal home folder.